Combining geometry-aware statistical and deep learning for neuroimaging data

该项目将开发在约束流形上构成非矢量结构化对象（对象数据）的数据的方法，这些数据在生物医学成像中起着关键作用。特别是，我们将重点关注两个重要的特殊情况：1)从功能磁共振成像（fMRI）获得的连接矩阵和2)从结构磁共振成像（MRI）获得的脑结构形状，它们作为输入（例如疾病分类）和输出（例如疾病标记）都是相关的。连通性矩阵是对称正定矩阵，形状是关于平移、旋转和/或尺度的等价类，但它们所依赖的黎曼流形的几何结构经常被忽略。例如，这可能导致对象输出在空间之外的无效预测（例如，非正定连接矩阵）和对象输入分类的次优结果。神经影像学数据的另一个挑战是混淆变量，如年龄或性别，这些变量通常无法控制，以及纵向研究中对象之间对同一主题的依赖性。进一步需要的是可解释的模型，这些模型可以帮助更好地理解健康结果、神经生物学标记和年龄或性别等其他因素之间的潜在关系，同时表现出良好的预测性能。在这个项目中，我们将为这两种类型的对象数据开发和基准测试方法，作为尊重其几何形状的输入或输出。我们结合了灵活的基于模型的统计学习方法的优势-可解释性，对混杂因素的调整和时间依赖结构-与深度学习的优势-特别是预测性能和可扩展的软件解决方案。为了更好地理解对象生物标志物与许多健康相关变量（包括年龄和疾病状态）之间的关系，通过建立更有效和可解释的模型，我们将在三个数据集中对这两种类型的对象数据进行测试。这些是1)英国生物银行和人类连接组项目中的fMRI连接矩阵，2)纵向阿尔茨海默病神经成像倡议数据库中的形状数据。

This project will develop methods for data that constitute non-vectorial structured objects (object data) lying on a constrained manifold, which play a key role in biomedical imaging. In particular, we will focus on the two important special cases: 1) connectivity matrices obtained from functional magnetic resonance imaging (fMRI) and 2) shapes of brain structures obtained from structural magnetic resonance imaging (MRI), which are relevant both as inputs (e.g. for disease classification) and as outputs (e.g. as disease markers). Connectivity matrices are symmetric positive definite matrices, and shapes are equivalence classes with respect to translation, rotation and/or scale, but the geometric structure of the Riemannian manifolds they live on is often ignored. This can lead for instance to invalid predictions outside the space (e.g. non positive definite connectivity matrices) for object outputs and suboptimal results in classification for object inputs. Additional challenges in neuroimaging data are confounding variables such as age or sex that are often not controlled for, and the dependence between objects on the same subject in longitudinal studies. A further desideratum are interpretable models that can aid in developing a better understanding of the underlying relationship between health outcomes, neurobiological markers and other factors such as age or sex, while showing good predictive performance.In this project, we will develop and benchmark methods for both types of object data as either inputs or outputs that respect their geometry. We combine the strengths of flexible model-based statistical learning approaches - interpretability, adjustment for confounders and temporal dependence structure - with those from deep learning - in particular predictive performance and scalable software solutions. To better understand the relationship of object biomarkers with a number of health-related variables including age and disease status, by building more valid and interpretable models, we will test these methods in three data sets for both types of object data. These are 1) fMRI connectivity matrices in the UK Biobank and the Human Connectome Project and 2) shape data in the longitudinal Alzheimer’s Disease Neuroimaging Initiative database.